The present invention relates to a microconnector with high contact density. It more particularly applies to low temperature electrical connections and, in the field of electronics and microelectronics, to high density miniaturised circuit connections. The Prior Art connectors making it possible to establish contacts between electrical conductors suffer from the following disadvantages. They only make it possible to obtain a limited contact density between the conductors and at the best a few dozen separate contacts with a spacing of approximately 1 mm, they occupy a significant volume, generally have a complicated structure with moving parts and a relatively high mass, so that they are unsuitable for use in a cryogenic environment and in a reduced space.